Abstract
The α-modeling strategy is followed to derive a new subgrid parameterization of the turbulent stress tensor in large-eddy simulation (LES). The LES-α modeling yields an explicitly filtered subgrid parameterization which contains the filtered nonlinear gradient model as well as a model which represents Leray-regularization. The LES-α model is compared with similarity and eddy-viscosity models that also use the dynamic procedure. Numerical simulations of a turbulent mixing layer are performed using both a second order, and a fourth order accurate finite volume discretization. The Leray model emerges as the most accurate, robust and computationally efficient among the three LES-α subgrid parameterizations for the turbulent mixing layer. The evolution of the resolved kinetic energy is analyzed and the various subgrid-model contributions to it are identified. By comparing LES-α at different subgrid resolutions, an impression of finite volume discretization error dynamics is obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Spalart, P.R.: 1988. Direct simulation of a turbulent boundary layer up to R0=1410. J. Fluid Mech. 187, 61.
Rogallo, R.S., Moin, P.: 1984. Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech. 16, 99.
Lesieur, M.: 1990. Turbulence influids. Kluwer Academic Publishers., Dordrecht.
Meneveau, C., Katz, J.: 2000. Scale-invariance and turbulence models for large-eddy simulation. Ann. Rev. Fluid Mech. 32, 1.
Germano, M.: 1992. Turbulence: the filtering approach. J. Fluid Mech. 238, 325.
Geurts B.J.: 1999 Balancing errors in LES. Proceedings Direct and Large-Eddy simulation III: Cambridge. Eds: Sandham N.D., Voke P.R., Kleiser L., Kluwer Academic Publishers, 1.
Vreman A.W., Geurts B.J., Kuerten J.G.M.: 1997. Large-eddy simulation of the turbulent mixing layer, J. Fluid Mech. 339, 357.
Vreman A.W., Geurts B.J., Kuerten J.G.M.: 1994. Realizability conditions for the turbulent stress tensor in large eddy simulation. J. Fluid Mech. 278, 351.
Ghosal, S.: 1999. Mathematical and physical constraints on large-eddy simulation of turbulence. AIAA J. 37, 425.
Holm, D.D., Marsden, J.E., Ratiu, T.S.: 1998. Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. in Math 137, 1.
Holm, D.D., Marsden, J.E., Ratiu, T.S.: 1998. Euler-Poincaré models of ideal fluids with nonlinear dispersion. Phys. Rev. Lett. 80, 4173.
Camassa, R., Holm, D.D.: 1993. An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661.
Chen, S.Y., Foias, C., Holm, D.D., Olson, E.J., Titi, E.S., Wynne, S.: 1998. The Camassa-Holm equations as a closure model for turbulent channel flow. Phys. Rev. Lett. 81, 5338.
Chen, S.Y., Foias, C., Holm, D.D., Olson, E.J., Titi, E.S., Wynne, S.: 1999. A connection between Camassa-Holm equations and turbulent flows in channels and pipes. Phys. Fluids 11, 2343.
Chen, S.Y., Foias, C., Holm, D.D., Olson, E.J., Titi, E.S., Wynne, S.: 1999. The Camassa-Holm equations and turbulence. Physica D 133, 49.
Chen, S.Y., Holm, D.D., Margolin, L.G., Zhang, R.: 1999. Direct numerical simulations of the Navier-Stokes alpha model, Physica D 133, 66.
Holm, D.D.: 1999. Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion. Physica D 133, 215.
Marsden, J.E., Shkoller, S.: 2001. The anisotropic Lagrangian averaged Navier-Stokes and Euler equations. Arch. Ration. Mech. Analysis. (In the press.)
Shkoller, S.: 1998. Geometry and curvature of diffeomorphism groups with H 1 metric and mean hydrodynamics. J. Func. Anal. 160, 337.
Marsden, J.E., Ratiu, T.S., Shkoller, S.: 2000. The geometry and analysis of the averaged Euler equations and a new diffeomorphism group. Geom. Funct. Anal. 10, 582.
Foias, C., Holm, D.D., Titi, E.S.: 2002. The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Diff. Eqs. to appear.
Marsden, J.E., Shkoller, S.: 2001. Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-α) equations on bounded domains. Phil. Trans. R. Soc. Lond. A 359, 1449.
Foias, C., Holm, D.D., Titi, E.S.: 2001. The Navier-Stokes-alpha model of fluid turbulence. Physica D 152 505.
Domaradzki, J.A., Holm, D.D.: 2001. Navier-Stokes-alpha model: LES equations with nonlinear dispersion. Modern simulation strategies for turbulent flow. Edwards Publishing, Ed. B.J. Geurts. 107.
Mohseni, K., Kosovic, B., Marsden, J.E., Shkoller, S., Carati, D., Wray, A., Rogallo, R.: 2000. Numerical simulations of homogeneous turbulence using the Lagrangian averaged Navier-Stokes equations. Proc. of the 2000 Summer Program, 271. Stanford, CA: NASA Ames/Stanford University.
Holm, D.D., Kerr, R.: 2001. Transient vortex events in the initial value problem for turbulence. In preparation.
Holm, D.D.: 1999. Alpha models for 3D Eulerian mean fluid circulation. Nuovo Cimento C 22, 857.
Bardina, J., Ferziger, J.H., Reynolds, W.C.: 1983. Improved turbulence models based on large eddy simulations of homogeneous incompressible turbulence. Stanford University, Report TF-19.
Leonard, A.: 1974. Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237.
Clark, R.A., Ferziger, J.H., Reynolds, W.C.: 1979. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1.
Vreman A.W., Geurts B.J., Kuerten J.G.M.: 1996. Large eddy simulation of the temporal mixing layer using the Clark model TCFD 8, 309.
Winckelmans, G.S., Jeanmart, H., Wray, A.A., Carati, D., Geurts, B.J.: 2001. Tensor-diffusivity mixed model: balancing reconstruction and truncation. Modern simulation strategies for turbulent flow. Edwards Publishing, Ed. B.J. Geurts. 85.
Leray, J.: 1934. Sur le mouvement ďun liquide visqueux emplissant ľespace tActa Math. 63, 193. Reviewed, e.g., in P. Constantin, C. Foias, B. Nicolaenko and R. Temam, Integral manifolds and inertial manifolds for dissipative partial differential equations. Applied Mathematical Sciences, 70, (Springer-Verlag, New York-Berlin, 1989).
Vreman A.W., Geurts B.J., Kuerten J.G.M.: 1995. A priori tests of Large Eddy Simulation of the compressible plane mixing layer. J. Eng. Math. 29, 299
de Bruin, I.C.C.: 2001. Direct and large-eddy simulation of the spatial turbulent mixing layer. Ph.D. Thesis, Twente University Press.
Germano, M., Piomelli U., Moin P., Cabot W.H.: 1991. A dynamic subgrid-scale eddy viscosity model. Phys. of Fluids 3, 1760
Geurts, B.J., Holm, D.D.: 2001. Leray simulation of turbulent flow. In preparation.
Ghosal, S.: 1996. An analysis of numerical errors in large-eddy simulations of turbulence. J. Comp. Phys. 125, 187.
Vreman A.W., Geurts B.J., Kuerten J.G.M.: 1996. Comparison of numerical schemes in Large Eddy Simulation of the temporal mixing layer. Int. J. Num. Meth. in Fluids 22, 297.
Vreman A.W., Geurts B.J., Kuerten J.G.M.: 1994. Discretization error dominance over subgrid-terms in large eddy simulations of compressible shear layers. Comm. Num. Meth. Eng. Math. 10, 785.
Geurts, B.J., Fröhlich, J.: 2001. Numerical effects contaminating LES: a mixed story. Modern simulation strategies for turbulent flow. Edwards Publishing, Ed. B.J. Geurts. 309.
Geurts B.J., Vreman A.W., Kuerten J.G.M.: 1994. Comparison of DNS and LES of transitional and turbulent compressible flow: flat plate and mixing layer. Proceedings 74th Fluid Dynamics Panel and Symposium on Application of DNS and LES to transition and turbulence, Crete, AGARD Conf. Proceedings 551:51
Ghosal, S., Moin, P.: 1995. The basic equations for large-eddy simulation of turbulent flows in complex geometry. J. Comp. Phys. 286, 229.
Du Vachat, R.: 1977. Realizability in equalities in turbulent flows. Phys. Fluids 20, 551.
Schumann, U.: 1977. Realizability of Reynolds-stress turbulence models. Phys. Fluids 20, 721.
Ortega, J.M.: 1987. Matrix Theory. Plenum Press. New York
Ghosal, S., Lund, T.S., Moin, P., Akselvoll, K.: 1995. A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286, 229.
Lilly, D.K.: 1992. A proposed modification of the Germano subgrid-scale closure method. Phys. of Fluids A 4, 633.
Geurts, B.J.: 1997. Inverse modeling for large-eddy simulation. Phys. of Fluids 9, 3585.
Kuerten J.G.M., Geurts B.J., Vreman, A.W., Germano, M.: 1999. Dynamic inverse modeling and its testing in large-eddy simulations of the mixing layer. Phys. Fluids 11, 3778.
Horiuti, K.: Constraints on the subgrid-scale models in a frame of reference undergoing rotation. J. Fluid Mech., submitted.
Germano, M.: 1986. Differential filters for the large eddy numerical simulation of turbulent flows. Phys Fluids 29, 1755.
Smagorinsky, J.: 1963. General circulation experiments with the primitive equations. Mon. Weather Rev. 91, 99.
Stolz, S., Adams, N.A.: 1999. An approximate deconvolution procedure for large-eddy simulation. Phys. of Fluids, 11, 1699.
Domaradzki, J.A., Saiki, E.M.: 1997. A subgrid-scale model based on the estimation of unresolved scales of turbulence. Phys. of Fluids 9, 1.
Wasistho, B., Geurts, B.J., Kuerten, J.G.M.: 1997. Numerical simulation of separated boundary layer flow. J. Engg. Math 32, 179.
Chatelin, F.: 1993. Eigen values of matrices. John Wiley & Sons. Chichester.
Jameson, A.: 1983. Transonic flow calculations. MAE-Report 1651, Princeton
Geurts, B.J., Kuerten, J.G.M.: 1993. Numerical aspects of a block-structured flow solver. J. Engg. Math. 27, 293.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
Geurts, B.J., Holm, D.D. (2002). Alpha-modeling Strategy for LES of Turbulent Mixing. In: Drikakis, D., Geurts, B. (eds) Turbulent Flow Computation. Fluid Mechanics and Its Applications, vol 66. Springer, Dordrecht. https://doi.org/10.1007/0-306-48421-8_7
Download citation
DOI: https://doi.org/10.1007/0-306-48421-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0523-7
Online ISBN: 978-0-306-48421-6
eBook Packages: Springer Book Archive